Your second interpretation is the correct one. When these machines are setup they are setup with pump lines... each line can only provide one chemical, so its optimial to get as much volume of that chemical out of that particualr line. What happens in many factories is they have two or more machines setup with a line to run chemical X because some days the volume required for chemical X is high enough to justify them all. In reality though this is very rarely the case, and proving that via an optimial solution of their previous 6 months data is the point of the exercise.

When you have mutiple machines setup with a line(nozzle) to run chemical X but you are not using them it is very costly, so again the idea would be to reduce the number of total lines by collapsing or consolidating all the lines for chemical X(,Y,Z,..n) respectively when there is volume enough available to cover demand on a fewer numebr of nozzles. You cannot colapse Y onto Z..so if we think of the backpack problem, you have 5 colors of weights and the weights can only be consolidated like legos (idk)with their own color.

Lets say chemical X is run on 5 machines, and on Tuesday you need 100 units of chemical X. The capacity for each machine is 50units per day, thus you would want to use 2 nozzles optimized rather than 4. If the capacity were 100, then the ideal answer would be to have only one nozzle-machine running chemical X, thus when you need X the other machines stay off and you only need that one machine to be on

I'm totally aware that my description (and understanding) is quite limmited and this is not helpful ( I'm really over my head here with a deadline otherwise Id buy a textbook and learn it the proper way). I very much appreciate you guys helping me anyways it has already been HUGELY helpful.

As far as data goes, I cannot provide the real data but will do my best to mock up a dummmy dataset that represents similar idea and post ASAP

Thanks again for bearing with me!

In reply to Re^2: Tricky chemicals optimization problem by Anonymous Monk
in thread Tricky chemicals optimization problem by Anonymous Monk

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